Haven't read all the responses yet, but she DID say that her kids have their own seats. That's not the issue with taking them onboard. The issue is that the seat has to be certified for an airplane, and even then it is at the airline's (actually, the flight attendant's) discretion whether they'll let you install it or not. My friend had purchased a car seat that was MADE for airplane travel (it also had a handle and foldout wheels to stroll around the airport (genius!)) and she was allowed to use it on a flight to her destination, but not back. No reason given.
because depending on the age of your kids they may not have their own seat! but in my case i was traveling with 2 six month old twins and needed the car seats and a snap and go to get them to the gate, but clearly could not take said items on board with me.
i still dont see what kind of damage you both are referring to that is going to make my seat less crash worthy. specially if i make a point of wrapping it up so they cant grab the thing by any straps